This paper examines a voxel (N-dimensional pixel) based representation for shape optimisation problems, and shows that although a basic genetic algorithm performed poorly on a simplified beam design problem, the use of three domain specific operators improved performance greatly. Additionally, the use of a `directed smoothing' operator that preferentially adds material to high stress areas was examined and found to assist evolutionary search. This paper demonstrates how domain knowledge and an understanding of how genetic algorithms work can be used to inform the design of suitable operators. 1. Introduction Shape optimisation within constraints is a hard problem from the field of Mechanical Engineering. The objective is to design a shape that best satisfies some predetermined goal whilst at the same time maintaining some property of the shape within a constraint, or perhaps even a set of constraints. Previous work has applied genetic algorithms (GAs) [1] to shape optimisation problem...

Abstract. This paper explores the potential of applying Genetic Algorithms to land use planning, a spatial allocation problem. Two genotype representations are proposed: a fixed-length genotype composed of genes that map directly to a land parcel's use, and a variable-length, order-dependent representation making allocations indirectly via a greedy algorithm. The fixed-length genotype is used within a standard genetic algorithm framework but the variable-length genotype requires novel breeding operators to be defined and post-processing of the genotype structure to identify and remove duplicate genotypes. The two approaches are compared on a real land use planning problem and the strengths and weaknesses of each approach are identified. Key Words: representation, messy GAs, non-fitness information, land use planning

. Shape optimisation is a hard problem from the field of Mechanical Engineering with the potential for significant cost savings if successfully performed. In the past, evolutionary optimisation approaches have proved successful. In those studies, a form of the shape was assumed, and its parameters optimised. An alternative is a voxel (N-dimensional pixel) based representation, which makes no such assumptions about the form of the solution, and allows the user to add domain knowledge if desired. This paper outlines a preliminary investigation into this approach and shows that the objections to this approach in the literature can be overcome if care is taken over the design of the operators. 1 Introduction Shape optimisation within constraints is a hard problem from the field of Mechanical Engineering. The objective is to design a shape which best satisfies some predetermined goal whilst at the same time maintaining some property of the shape within a constraint, or perhaps even a set o...

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